Algebra Examples

$\frac{\frac{x + 3}{x - 3}}{\frac{x^{2} - 9}{3 x - 9}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{x + 3}{x - 3} \cdot \frac{3 x - 9}{x^{2} - 9}$

Step 2

Factor $3$ out of $3 x - 9$ .

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Step 2.1

Factor $3$ out of $3 x$ .

$\frac{x + 3}{x - 3} \cdot \frac{3 (x) - 9}{x^{2} - 9}$

Step 2.2

Factor $3$ out of $- 9$ .

$\frac{x + 3}{x - 3} \cdot \frac{3 x + 3 \cdot - 3}{x^{2} - 9}$

Step 2.3

Factor $3$ out of $3 x + 3 \cdot - 3$ .

$\frac{x + 3}{x - 3} \cdot \frac{3 (x - 3)}{x^{2} - 9}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $9$ as $3^{2}$ .

$\frac{x + 3}{x - 3} \cdot \frac{3 (x - 3)}{x^{2} - 3^{2}}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$\frac{x + 3}{x - 3} \cdot \frac{3 (x - 3)}{(x + 3) (x - 3)}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $x + 3$ .

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Step 4.1.1

Cancel the common factor.

$\frac{x + 3}{x - 3} \cdot \frac{3 (x - 3)}{(x + 3) (x - 3)}$

Step 4.1.2

Rewrite the expression.

$\frac{1}{x - 3} \cdot \frac{3 (x - 3)}{x - 3}$

Step 4.2

Cancel the common factor of $x - 3$ .

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Step 4.2.1

Factor $x - 3$ out of $3 (x - 3)$ .

$\frac{1}{x - 3} \cdot \frac{(x - 3) \cdot 3}{x - 3}$

Step 4.2.2

Cancel the common factor.

$\frac{1}{x - 3} \cdot \frac{(x - 3) \cdot 3}{x - 3}$

Step 4.2.3

Rewrite the expression.

$\frac{3}{x - 3}$